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[Impaler[WrG]]

I've noticed that DF generates rock based on a 48x48 grid system, you can see it quite clearly with reveal.exe, each of these squares is filled with some type of 'layer' rock and secondary minerals such as ores and gems.  Their are three general types, large clusters, veins and small clusters.  If one is primarily interested in finding veins which hold the lions share of all valuable metals you want to maximize the chance you will 'strike' a vein while minimizing the amount of rock needed to make the strike.  The wiki currently lists a 15x15 block technique as its highest labor efficiency at 12% of all rock mined.  But by taking the grid pattern into account a superior exploratory mining technique can be designed.

Steps

1 - Orient your self to the center or near center of one of the 48x48 blocks, this can be done by counting manualy from the edge of the map or finding the center of a large cluster of rock as these are centered on the grid.
2 - Dig a vertical staircase strait down through the center of the block
3 - On any level ware you hit a large cluster type stone skip it as their will be no vein in that block
4 - On the other levels dig a + shaped cross outward from the staircase with each leg 12 tiles long for a total mined area of 48 tiles per z level.

This should work because the veins have a very high probability of intersecting this + shape due to their length, though it is possible that very short or 'bent' veins could elude you.  The main benefit is a very high labor efficiency, if we consider the whole block of 2304 tiles is checked with 48 tiles mined out a mere 2% of the total rock (without factoring the considerable savings from skipping Large Cluster filled areas) and I'd estimate 75% of all veins will be struck.  If future expansion is desired its easy to upgrade to denser forms of mining like 15x15 blocks or extending branches off the + shape to get at those few remaining hidden veins.

If anyone is interested in trying this pattern and then run map reveal and compare how many veins were found with how many were missed. 

[sneakey pete]

Also a good method to go about with when looking for map features (chasm, magma, ponds, HFS)

[Dorten]

There also are cases, when a vein goes through cluster, for example platinum in magnetite. (Though you will strip-mine the cluster in this case anyway, but you need to check the raws for other possible combinations)

[sneakey pete]

platinum in olivine too.

[Rilder]

Not very dwarvenly, requires magma.

[Philosophical Gamer]

I used a method for awhile which I think is more efficient than the block method, using diagonal-direction digging.  It's a bitch to designate but it's very, very fast.

Something like this:

XOOOXOOOOOXOOO
OXOXOOOOOXOOOO
OOXOOOOOXOOOOO
OXOXOOOXOOOOOX
XOOOXOXOOOOOXO
OOOOOXOOOOOXOO
OOOOXOXOOOXOOO
OOOXOOOXOXOOOO
OOXOOOOOXOOOOO

X=Dug Square
O=Non-Dug Square

You end up seeing every single square in a very short amount of time.

I don't know if this is more efficient, but I liked it.

[Milskidasith]

The best method, and a pretty damn easy one to set up, for exploratory mining is shaft mining.

XXXXXXXXX
XOXXOXXOX
XXXXXXXXX
XXXXXXXXX
XOXXOXXOX
XXXXXXXXX
XXXXXXXXX
XOXXOXXOX

Etc. (O is mined out). 100% reveal with very very little labor (for a 48 by 48 square it probably matches the labor of his cross design and is easy to set up).

You just need lots of staircases and an entire layer of rock mined out to explore the whole world with this.

[Impaler[WrG]]

The wiki already mentions both the diagonal and vertical shaft as exploration techniques, both are 100% revealing techniques aimed at finding all gems which is not the scope of what I'm proposing.  The diagonal method has an efficiency of 20% (1/5th of all squares mined) (BTW PG your picture is slightly different then the official method as you spaced the tunnels 5 spaces apart which would leave one unrevealed tile per cube, thats probably worth it though considering how rare a lone crystal is).  The vertical shaft method has an efficiency of 11%(1/9th all squares mined) which is considerably more mining then my proposed 2% solution. 

But it also gives me an idea, it should be possible to combine the two methods and mine in a linear row of shafts rather then a tunnel.  You would mine a + at just one level and then sink shafts every 4 spaces along the legs with the first one 5 tiles from the center of the + for a total of just 16 shafts per cubic area, a mind boggling 0.7% of all rock mined to find almost all veins.